J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... decidability of bisimilarity for BPP was given in [8] while all other equivalences in van Glabbeek s spectrum are undecidable in BPP [15, 17] In order to deal with timing aspects of systems, process algebras were extended with an appropriate notion of time (see e.g. 20] 1] 14] 10] 9] [2]) A substantial effort have also been directed toward defining a robust notion of equivalence taking performance into consideration, e.g. equivalence that relates only those processes that exhibit the same behavior at the same speed. The bisimilarity investigated in [14, 10, 9] applies to ....

J. Baeten and C. Middelburg. Process algebra with timing: real time and discrete time. In J. Bergstra, A. Ponse, S. Smolka, eds., Handbook of Process Algebra, chapter 10, pages 627-- 684, 2001.

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J.C.M. Baeten, C.A. Middelburg, Process algebra with timing: Real time and discrete time, in: J.A. Bergstra, A. Ponse, S.A. Smolka (Eds.), Handbook of Process Algebra, Elsevier, Amsterdam, 2001 (Chapter 10).

.... the new equivalence (Sections 6 and 7) Then, we continue the analysis using the new axioms (Section 8) Finally, some concluding remarks are made (Section 9) 2 Process Algebraic Preliminaries The version of process algebra with discrete relative timing used in Sections 3, 4 and 5 is ACP [3] extended with abstraction and guarded recursion. This section gives a brief summary. For reference, the axioms are given in Appendix A. For a comprehensive overview of ACP guarded recursion, the reader is referred to [4] In the case of ACP , timing is relative to the time at which the ....

J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra, pages 627-684. Elsevier, Amsterdam, 2001.

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J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra, pages 627-684. Elsevier, 2001.

....is easy to see that carrying on in this way, we can reduce any TSS that de nes parametrized transition relations to a TSS that only de nes unparametrized unary and binary transition relations, while preserving bisimilarity. Example 5. 1 In Appendix A, a TSS of BPA sat with integration (see [5]) is given. It is a TSS that de nes parametrized transition relations. The sort R 0 of non negative real numbers and the sort P(R 0 ) of sets of non negative real numbers are considered given sorts. There is one transition rule with a negative premise. Moreover, a variable binding operator, viz. ....

....constants remain distinct, calculus features such as input action pre xes x(y) and the restriction operator could be dealt with as well. Our main motivation to take up the work presented in this paper stems directly from work on an integrated treatment of all versions of ACP with timing [5]. That work created the need of a generalization of the framework from [38] that takes variable binding operators and many sortedness into account. The notion of TSS was already generalized to deal with variable binding operators and many sortedness in [17] That paper gives syntactic criteria for ....

J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier, 2000.

....Timing Next, we look at extensions of the theory presented in the previous section. Especially important is the addition of timing features. First, we consider process algebra with real time in relative timing (see [1] Further on, we look at discrete timing. We use the treatment and notation of [4], since it allows a smooth integration of real time and discrete time theories, and also allows separation of actions and timing information. The framework of [4] allows for an integrated treatment of all process algebras with timing. Notice that this treatment for dense time contains so called ....

....algebra with real time in relative timing (see [1] Further on, we look at discrete timing. We use the treatment and notation of [4] since it allows a smooth integration of real time and discrete time theories, and also allows separation of actions and timing information. The framework of [4] allows for an integrated treatment of all process algebras with timing. Notice that this treatment for dense time contains so called urgent actions, which means that more than one action can occur consecutively at the same moment of time. Of course, this is an abstraction of reality (but a useful ....

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J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier Science, Amsterdam, 2000. To appear.

....basic theory, several improvements could be made. The main reason for the reformulation becomes evident, however, when we consider timing. It is not necessary to look at the whole framework of discrete and dense timed, absolute and relative timed, time stamped and two phase process algebras (see [5]) Instead, we can make the point by considering one member of this family, viz. process algebra with discrete time in relative timing in two phase notation (see [4] Also, it is su#cient to consider the theory without parallel composition. We have the following syntax in addition to signature ....

J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier Science, Amsterdam, 2000. To appear.

....that it means that processes are supposed to be capable of performing certain actions, like in time free process algebra, as well as passing to the next time slice. A coherent collection of versions of ACP with timing where performance of actions and passage of time are separated, is presented in [7]. First we treat the basic discrete relative time process algebra BPA drt ID. Then we treat PA drt ID, the extension of BPA drt ID with parallel composition in which no communication between processes is involved. ACP drt ID, the extension of BPA drt ID with parallel composition in which ....

J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: Real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier, 2000. Chapter 4.1 in this issue.

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J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: real time and discrete time. In J.A. Bergstra, A. Ponse, and S.A. Smolka, editors, Handbook of Process Algebra. Elsevier, 1999.

No context found.

J.C.M. Baeten, C. A. Middelburg, Process algebra with timing: Real time and discrete time, Eindhoven University of Technology, CSR 99-11, 1999. To appear in J.A. Bergstra, A. Ponse and S.A. Smolka, ed., Handbook of Process Algebra, Elsevier, 2000.

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